Litespeed executes from an extended procedure - which creates a new connection to the database to perform the backup. By default, the service account running SQL Server Agent does not have any permissions and is not included as a login...the login that is included is the virtual account NT SERVICE\SQLSERVERAGENT.
To allow Litespeed to perform the backups - the account running the backup needs to be added as a login with appropriate permissions. The Litespeed documentation should identify the minimum permissions but it will likely need sysadmin.
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